{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第一次作业"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0o2fCFeKZwDY7vQfolEtRVe8C7gLzyRl27RxDht5o947QWHrcBJYeNyHa1XBE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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a6934289b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import math\n",
    "\n",
    "def rotateList(x1, y1, rx, ry, a):\n",
    "    a = math.radians(a)\n",
    "    x2 = [round((x1i-rx)*math.cos(a) - (y1i-ry)*math.sin(a) + rx,4) for (x1i, y1i) in zip(x1, y1)]\n",
    "    y2 = [round((x1i-rx)*math.sin(a) + (y1i-ry)*math.cos(a) + ry,4) for (x1i, y1i) in zip(x1, y1)]\n",
    "    return x2,y2\n",
    "\n",
    "def rotate(x1, y1, rx, ry, a):\n",
    "    a = math.radians(a)\n",
    "    x2 = round((x1-rx)*math.cos(a) - (y1-ry)*math.sin(a) + rx,4)\n",
    "    y2 = round((x1-rx)*math.sin(a) + (y1-ry)*math.cos(a) + ry,4)\n",
    "    return x2,y2\n",
    "\n",
    "x1 = [1,2,3,1]\n",
    "y1 = [1,3,0,1]\n",
    "x2, y2 = rotateList(x1, y1, 0, 0, 45)\n",
    "x3, y3 = rotateList(x1, y1, 0, 0, 90)\n",
    "x4, y4 = rotateList(x1, y1, 0, 0, 180)\n",
    "x5, y5 = rotateList(x1, y1, 2, 1, 30)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(321)\n",
    "ax2 = fig.add_subplot(322)\n",
    "ax3 = fig.add_subplot(312)\n",
    "ax4 = fig.add_subplot(325)\n",
    "ax5 = fig.add_subplot(326)\n",
    "\n",
    "ax1.plot(x1, y1)\n",
    "ax1.set_title('原始图形')\n",
    "ax2.plot(x2, y2)\n",
    "ax2.set_title('绕原点旋转45度')\n",
    "ax3.plot(x3, y3)\n",
    "ax3.set_title('绕原点旋转90度')\n",
    "ax4.plot(x4, y4)\n",
    "ax4.set_title('绕原点旋转180度')\n",
    "ax5.plot(x5, y5)\n",
    "ax5.set_title('绕点（2,1）旋转30度')\n",
    "\n",
    "fig.suptitle('第一、二题作业')\n",
    "fig.subplots_adjust(hspace=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3zAGEE0WLcprmyJH8S0X89x97g6VLm9RDuNCiBfD448CkSQzTzA/z51OGulcv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\nMMUcgGEYRpjyf+fIlHYbmmBhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x180e9c42b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from pylab import *\n",
    "import math\n",
    "mpl.rcParams['font.sans-serif'] = ['SimHei'] #指定默认字体\n",
    "mpl.rcParams['axes.unicode_minus'] = False   #解决保存图像是负号'-'显示为方块的问题\n",
    "\n",
    "def rotateList(x1, y1, rx, ry, a):\n",
    "    a = math.radians(a)\n",
    "    x2 = [round((x1i-rx)*math.cos(a) - (y1i-ry)*math.sin(a) + rx,4) for (x1i, y1i) in zip(x1, y1)]\n",
    "    y2 = [round((x1i-rx)*math.sin(a) + (y1i-ry)*math.cos(a) + ry,4) for (x1i, y1i) in zip(x1, y1)]\n",
    "    return x2,y2\n",
    "\n",
    "def rotate(x1, y1, rx, ry, a):\n",
    "    a = math.radians(a)\n",
    "    x2 = round((x1-rx)*math.cos(a) - (y1-ry)*math.sin(a) + rx,4)\n",
    "    y2 = round((x1-rx)*math.sin(a) + (y1-ry)*math.cos(a) + ry,4)\n",
    "    return x2,y2\n",
    "\n",
    "def gen_circle_point(n):\n",
    "    ai = 360/(n+1)\n",
    "    if n % 2 == 0:\n",
    "        a = ai * (n-2)/2\n",
    "    else:\n",
    "        a = ai * (n-3)/2\n",
    "        \n",
    "    x, y = 0, 1\n",
    "    flag = 0\n",
    "    p1 = [[],[]]\n",
    "    p2 = [[],[]]\n",
    "    for i in range(0, n+2):\n",
    "        x_old, y_old = x, y\n",
    "        x, y = rotate(x, y, 0, 0, a)\n",
    "        p2[0].append(x)\n",
    "        p2[1].append(y)\n",
    "        p1[0].append((x+x_old)/2)\n",
    "        p1[1].append((y+y_old)/2)\n",
    "        \n",
    "    return (p1, p2)\n",
    "    \n",
    "\n",
    "N=10\n",
    "\n",
    "p1,p2 = gen_circle_point(N-1)\n",
    "plt.plot(p1[0],p1[1],'b.')\n",
    "plt.plot(p2[0],p2[1],'r')\n",
    "plt.axis('equal')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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S0p/o0+cphg791mVxN+LjM5qQ4LvJyf2U6uoDZx23WSyU5WR3y/i7keYe/EyaF8yoB/pj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\ngkId5v8BjwAZHZuBgN8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a8dd2b3a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import math\n",
    "\n",
    "def rotate_list(x1, y1, rx, ry, a):\n",
    "    a = math.radians(a)\n",
    "    x2 = [(xi-rx)*math.cos(a) - (yi-ry)*math.sin(a) + rx for xi, yi in zip(x1, y1)]\n",
    "    y2 = [(xi-rx)*math.sin(a) + (yi-ry)*math.cos(a) + ry for xi, yi in zip(x1, y1)]\n",
    "    return x2,y2\n",
    "    \n",
    "x1 = [1, 2, 3, 1]\n",
    "y1 = [1, 3, 0, 1]\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.set_aspect(1)\n",
    "\n",
    "for a in range(0, 360, 30):\n",
    "    x, y = rotate_list(x1, y1, 2, 2, a)\n",
    "    ax.plot(x, y)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2.1213203435596424, -4.440892098500626e-16, 2.1213203435596433, -3.0, 2.1213203435596415, 1.7763568394002505e-15, -2.121320343559644, 3.0, -2.1213203435596406] [2.121320343559643, -3.0, 2.121320343559642, 1.3322676295501878e-15, -2.1213203435596437, 3.0, -2.121320343559641, -2.4424906541753444e-15, 2.1213203435596446]\n"
     ]
    },
    {
     "data": {
      "image/png": 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OAgIlSwIzZ9Lt8OGHNPShoSwQPX8+J0+zIzaW/rZevfglBBqRkVRGZ0O9qCj6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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a8dcf66898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import math\n",
    "def rotate(x, y, a):\n",
    "    a = math.radians(a)\n",
    "    return x*math.cos(a)-y*math.sin(a),y*math.cos(a)+x*math.sin(a)\n",
    "def rotatelist(x, y, a):\n",
    "    xx = []\n",
    "    yy = []\n",
    "    for (x1, y1) in zip(x, y):\n",
    "        x2, y2 = rotate(x1, y1, a)\n",
    "        xx.append(x2)\n",
    "        yy.append(y2)\n",
    "    return xx, yy\n",
    "def gen_circle_point(n):\n",
    "    a = 90 + 360.0/(n+1)\n",
    "    x = 3\n",
    "    y = 0\n",
    "    xx = []\n",
    "    yy = []\n",
    "    for i in range(0, n+2):\n",
    "        x , y = rotate(x, y, a)\n",
    "        xx.append(x)\n",
    "        yy.append(y)\n",
    "    print(xx, yy)\n",
    "    return xx, yy\n",
    "x = [1,2,3,1]\n",
    "y = [1,3,0,1]\n",
    "fig = plt.figure(1, figsize=(6,6))\n",
    "ax1 = fig.add_subplot(221) \n",
    "ax2 = fig.add_subplot(222)\n",
    "for a in range(0, 360, 90):\n",
    "    xx, yy = rotatelist(x,y,a)\n",
    "    ax1.plot(xx, yy,color='b',linewidth=2,linestyle='--',marker='D')\n",
    "fig = plt.figure(1, figsize=(6,6))\n",
    "xx, yy = gen_circle_point(7)\n",
    "ax2.plot(xx,yy,'r')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
